1. Field of the Invention
The present invention relates to a method for estimating natural frequency of a distribution system by performing a frequency analysis on an actually measured current in order to identify a rectifier load generating commutation oscillation.
2. Description of Related Art
Recently, increasing number of rectifier loads, such as inverters for motors and power supplies for computers, in which AC voltage is once converted into DC voltage, have been in use. The increase in the number of rectifier loads presents a problem in that harmonics generated by the rectifier loads will induce misoperation of other machines connected to the same distribution system, and generate abnormal sound or heat in a power factor improving capacitor.
Such harmonics are induced by commutation oscillation in a distribution system caused by notching voltage accompanying the commutation of a rectifier load. Thus, the source (a particular rectifier load) of the commutation oscillation must be identified before appropriate steps to restrict the harmonics are taken.
The mechanism by which harmonics are produced is as follows: First, notching voltage, which refers to dips on the order of 1 ms wide in a line-to-line voltage, is produced by the commutation of a rectifier load like a thyristor converter. The notching voltage induces free oscillation in an LC loop formed by the line inductance and a power factor improving capacitor connected to the distribution system. This free oscillation generates harmful harmonics in the distribution system. Such oscillation in the system triggered by the commutation is referred to as commutation oscillation. The commutation oscillation occurs in a quasi-stable manner. For example, when the number of rectifier phases in the three-phase full conversion is six, the commutation oscillation occurs six times during each period, and when it is twelve to reduce pulsation, the commutation oscillation takes place 12 times during each period.
The identification of a rectifier load that generates harmful harmonics is carried out by several methods. One of them is disclosed by Matsumura, Shinohara, and Naito, "Study of a method for identifying the source of harmonics in an overhead high voltage distribution system", Technical Research Reference of the Institute of Electric Power Engineers of Japan, PE-90-90 (1990), Japanese Patent Application Laying-open No. 64372/1993, and Japanese Patent Application Laying-open No. 67727/1992, which are incorporated here by reference. The outline of this method is as follows: First, a charging current flowing into a power factor improving capacitor is measured. Second, a frequency analysis of the measured current is carried out to obtain a local frequency. Third, a numerical analysis of a simulation circuit of the distribution system is performed to obtain the natural frequency of the distribution system. Finally, the local frequency is compared with the natural frequency to identify the rectifier load causing the harmonics.
More specifically, the waveform of the charging current flowing into the power factor improving capacitor is measured by a current transformer mounted on one of the power factor improving capacitors connected to the distribution system. A frequency analysis of the waveform is made in order to obtain resonant frequencies and amplitudes at these frequencies in respective generation modes that actually take place.
Next, a natural mode is obtained whose resonant frequency is substantially the same as that of each one of the generation modes by using a numerical simulation circuit of the distribution system. It is supposed that a rectifier load that generates a harmonic of that resonant frequency, which is induced by the commutation oscillation, will exist near the nodes which have a sharp response (sensitivity) in the natural mode. In other words, the rectifier load is not supposed to exist near the nodes which have a sensitivity less than a predetermined lower limit. Such nodes are successively excluded from the candidates to narrow down the nodes, thereby identifying the rectifier load that generates the commutation oscillation.
FIG. 1 is a schematic diagram of a device measuring a charging current of a power factor improving capacitor, and processing the measured current.
In this figure, distribution lines 1 are, for example, of a three phase, 6.6 kV distribution system. A power factor improving capacitor 2 is connected to the distribution lines 1. A current transformer 3 is mounted on one of the terminal leads of the power factor improving capacitor 2. The current flowing into the power factor improving capacitor 2 is measured with the current transformer 3, and is applied to an isolating amplifier 4.
The output of the isolating amplifier 4, that is, the input signal to an A/D converter 5 is an analog signal directly proportional to the charging current of the power factor improving capacitor 2, and includes harmonics on the order of several kilohertz generated on the normal frequency component by commutation oscillation. The A/D converter 5 samples the input signal at a predetermined interval, and converts it into a digital signal. The digital signal is sequentially stored in a memory of a computer 6.
The current transformer 3 is readily mounted on the power factor improving capacitor 2. This is because the capacitor 2 is installed in substation equipment of a customer which is supplied with power from the distribution system, and hence the power factor improving capacitor 2 can be easily placed in dead state while mounting the current transformer 3 on the terminal lead of the capacitor 2.
FIG. 2 illustrates a waveform of the charging current measured at the power factor improving capacitor 2 connected to the distribution system. To this distribution system, a rectifier load whose number of rectifier phases is twelve is also connected. The waveform was obtained by outputting the digital data stored in the memory of the computer 6.
In FIG. 2, the axis of abscissas represents time, and the axis of ordinates represents current values. The range along the time axis corresponds to one period T of the fundamental component. In this case, since the normal frequency of the distribution system is 50 Hz, the period T is 20 ms. As is clear from this figure, the measured charging current includes many harmonic components.
FIG. 3 is a graph illustrating the result of a frequency analysis of the charging current shown in FIG. 2. This frequency analysis was carried out by expanding the data D1 corresponding to the charging current of FIG. 2 into a Fourier series. In this graph, the axis of abscissas represents frequency, and the axis of ordinates represents the amplitude of harmonic components of respective orders. The amplitude is generally represented in terms of the ratio of the amplitude of the individual harmonic components to that of the fundamental component.
The natural frequency fr of the distribution system can be obtained from the frequency that gives a local peak amplitude in the graph.
If the distribution system and loads are in the three-phase balanced conditions, and the commutation oscillations of rectifiers occur exactly at the interval of T/N (where N is the number of rectifier phases), the orders of the harmonic components obtained by the frequency analysis, in which the charging current is expanded into a Fourier series, are limited to the following:
n=kN.+-.1 (1) PA1 n: the order of harmonics PA1 k: natural numbers beginning from 1 PA1 N: the number of rectifier phases (the number of commutations during each cycle) PA1 measuring a charging current flowing into the power factor improving capacitor; PA1 forming first data corresponding to the charging current; PA1 removing a fundamental component of the charging current from the first data to form second data; PA1 determining an interval, during which third data is picked up from the second data; and PA1 performing frequency analysis on the third data to form fourth data to determine a frequency corresponding to a local peak of the fourth data as the natural frequency of the distribution system. PA1 determining a first time at which the amplitude of the second data takes a maximum value; and PA1 determining the interval beginning from the first time and ending at a second time which is T/N later than the first time.
where
In practice, other order harmonics may occur owing to imbalance of the system impedance, or inequality of commutation interval. In general, however, these harmonics have much smaller amplitude than the harmonics satisfying equation (1). Accordingly, when the natural frequency fr is out of the frequency associated with the order n satisfying equation (1), the natural frequency fr will not be detected because it does not constitute a local peak. This presents a problem in that estimation accuracy of the natural frequency is degraded.